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Simplifying 12x2 + -27x + 5 = 0 Reorder the terms: 5 + -27x + 12x2 = 0 Solving 5 + -27x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.4166666667 + -2.25x + x2 = 0 Move the constant term to the right: Add '-0.4166666667' to each side of the equation. 0.4166666667 + -2.25x + -0.4166666667 + x2 = 0 + -0.4166666667 Reorder the terms: 0.4166666667 + -0.4166666667 + -2.25x + x2 = 0 + -0.4166666667 Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000 0.0000000000 + -2.25x + x2 = 0 + -0.4166666667 -2.25x + x2 = 0 + -0.4166666667 Combine like terms: 0 + -0.4166666667 = -0.4166666667 -2.25x + x2 = -0.4166666667 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = -0.4166666667 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = -0.4166666667 + 1.265625 Combine like terms: -0.4166666667 + 1.265625 = 0.8489583333 1.265625 + -2.25x + x2 = 0.8489583333 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 0.8489583333 Calculate the square root of the right side: 0.921389349 Break this problem into two subproblems by setting (x + -1.125) equal to 0.921389349 and -0.921389349.Subproblem 1
x + -1.125 = 0.921389349 Simplifying x + -1.125 = 0.921389349 Reorder the terms: -1.125 + x = 0.921389349 Solving -1.125 + x = 0.921389349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 0.921389349 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 0.921389349 + 1.125 x = 0.921389349 + 1.125 Combine like terms: 0.921389349 + 1.125 = 2.046389349 x = 2.046389349 Simplifying x = 2.046389349Subproblem 2
x + -1.125 = -0.921389349 Simplifying x + -1.125 = -0.921389349 Reorder the terms: -1.125 + x = -0.921389349 Solving -1.125 + x = -0.921389349 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -0.921389349 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -0.921389349 + 1.125 x = -0.921389349 + 1.125 Combine like terms: -0.921389349 + 1.125 = 0.203610651 x = 0.203610651 Simplifying x = 0.203610651Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.046389349, 0.203610651}
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